How NOT to show $P \implies Q$. Here is an argument that shows that if $n^2$ is even, then $n$ is
even
Proof. If $n^2 = 4$, then $n = 2$. If $n^2 = 16$, then $n = 4$. If $n^2 = 36$, then $n = 6$, and so on. This
implies that whenever $n^2$ is even, then $n$ must be even. The proof is complete.
Is the proof valid? Can you say why or why not?
